cause there is no expansion arall, if there is no change of volume; and it would be more accu rate to designate this fraction as the "coefficient of increase of pressure" at constant volume). It appears, therefore, that the temperature of melting ice, on the scale of the constant-volume gas thermometer, is numerically equal to 100 times the reciprocal of the coefficient of ex pansion of the gas at constant volume. Having found T., we have only to subtract it from every reading of the gas thermometer, in order to reduce that reading to its corresponding value as reckoned from the freezing point of water. If we call the values of T — T., as computed for any given gas thermometer, the "reduced readings" of that thermometer, then we find that the reduced readings of the nitro gen, hydrogen, air and carbon dioxide constant volume thermometers are all nearly identical, and that they are all closely comparable with the readings of the ordinary mercury-in-glass thermometer. If two constant-volume gas thermometers be filled with the same gas in dif ferent states of density, then the reduced read ings of the two are very nearly equal, but yet not necessarily identical.
The coefficients of expansion at constant volume of certain of the more important ther mometric gases are given in Table 1, as de duced from a careful analysis of the data given by Chappuis, Regnault and numerous other ex perimenters of high standing. The "initial pressure" signifies the pressure on the gas in the thermometric bulb, when the bulb is sur rounded by ice and water; this pressure being given as the most convenient way of fixing the density for which the, coefficients were deter mined. Two coefficients are given for air at each initial pressure, because it appears to be impossible to decide, from the observations thus far made, which one of these values is most likely to be correct, the available measures falling into two general groups, one of which favors one of the foregoing values, while the second favors the other one. In Table 1 the values of T. are also given, for convenience of reference.
The International Committee of Weights and Measures, in consideration of the differ ences that exist even between the reduced read ings of constant-volume gas thermometers, adopted the following standard scale for the measurement of temperature, calling it their "normal thermometric scale." The scale adopted is the Centigrade scale of the con stant-volume hydrogen thermometer, in which the hydrogen has a density such that its pressure, at the freezing point of water, is equal to that due to a column of ice-cold mercury, one metre (1,000 mm.) high. The tempera tures are understood to be "reduced," as de scribed above, so that the thermometer reads 0° at the freezing point and 100° at the boiling point. The ideal scale would of course be the absolute thermodynamic scale (see THERMODY NAMICS) ; but the corrections that are required in order to reduce gas thermometer readings to this scale are still too uncertain to be definitely adopted in nrecise thermometry.
In Table 2 comparative readings are given, of the mercury-in-glass ("verre dur"; see THERMOMETER) scale, and the scales of the con stant-volume hydrogen, nitrogen and carbon dioxide thermometers, in which the "initial pres sures" are 1,000 millimetres of mercury. The significance of the table will be made plain by the following example: If all df These ther mometers were exposed to a temperature at which the "reduced" reading of the hydrogen instrument was 30° C., then the nitrogen ther mometer would read 30.011° the Carbon dioxide thermometer would read and mercury in-glass thermometer would read 30.102°. The readings given in the second column were ob tained from experiments made upon the nitro gen thermometer; but Chappdts states that the reduced readings of the air thermometer and of the nitrogen thermometer are practically in distinguishable; and hence this column will serve for each of them.
In the constant-pressure gas thermometer, temperature is defined as proportional to the volume of a fixed mass of gas which is allowed to expand in such a manner that its pressure remains constant. Regnault experimented with thermometers of this class, and considered them to be distinctly inferior in accuracy to those in which the volume is constant, and which we have already described. This judgment pro nounced by Regnault has met with the approval of nearly every subsequent authority, upon ex perimental physics, and hence the constant pressure gas thermometer has not been at all extensively used in practical work. Professor H. L. Callendar, in fact, is almost the only prominent advocate of the constant-pressure in strument at the present time. He claims that the constant-pressure gas thermometer is capable of yielding results even superior to those of the constant-volume thermometer; and he has devised a very ingenious form of the constant-pressure instrument, which certainly appears to overcome most of the objections that have been urged against it in the past. (Con sult his paper entitled (On a Practical Ther mometric Standard,' in 'the Philosophical Magazine, for 1899, Vol. 48, page 519. Consult also, (Proceedings of the Royal Society,' Vol: 50, 1892, page 247, and Preston, (Theory of Heat)). To facilitate computation.s connected with the constant-pressure gas thermometer, we present, in Table 3, the coefficients of expansion of the principal thermometric gases at the con stant pressure of 1,000 millimeters of mercury and also at 760 millimeters. These are obtained by a careful comparison of the best determina tions that have yet been made.